SOLUTION: Solve for x. 5sec x + [tan x/cos x] = 0

You want to solve

     +  = 0.


The domain of this equation are all real numbers except of  x = ,
where cos(x) = 0.


In the domain, multiply both sides by  cos(x).


Since cos(x) =/= 0, you get an equivalent equation

    5 + tan(x) = 0.

which is the same as  

    tan(x) = -5.


Hence,  x = arctan(-5) +  = -arctan(5) +  = -1.37340077 +   radians, k = 0, +/-1, +/-2, . . .


ANSWER.  The general solution to the given equation is the set x = -arctan(5) +  = -1.37340077 +   radians, k = 0, +/-1, +/-2, . . .